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What is the Gaussian function?

A box contains 24 identical balls, of which 12 are black and 12 are white. The balls are drawn at random from the box one at a time with replacement. The probability that white ball is drawn for the fourth time on seventh draw is,

A). \[\dfrac{5}{{64}}\]

B). \[\dfrac{{27}}{{32}}\]

C). \[\dfrac{5}{{32}}\]

D). \[\dfrac{1}{2}\]

A). \[\dfrac{5}{{64}}\]

B). \[\dfrac{{27}}{{32}}\]

C). \[\dfrac{5}{{32}}\]

D). \[\dfrac{1}{2}\]

A contest consists of predicting the results of win, draw or defeat of 7 football matches. A sent his entry by predicting at random. The probability that his entry will contain exactly 4 correct predictions is

A). \[\dfrac{8}{{{3^7}}}\]

B). \[\dfrac{{16}}{{{3^7}}}\]

C). \[\dfrac{{280}}{{{3^7}}}\]

D). \[\dfrac{{560}}{{{3^7}}}\]

A). \[\dfrac{8}{{{3^7}}}\]

B). \[\dfrac{{16}}{{{3^7}}}\]

C). \[\dfrac{{280}}{{{3^7}}}\]

D). \[\dfrac{{560}}{{{3^7}}}\]

Two tetrahedral dice with faces marked 1, 2, 3 and 4 are thrown. The score obtained is the sum of the numbers on the bottom face. Calculate the probability distribution for the score obtained and how?

A man makes attempts to hit the target. The probability of hitting the target is $\dfrac{3}{5}$. Then, the probability that A hits the target exactly $2$ times in $5$ attempts is:

(A) $\dfrac{{144}}{{625}}$

(B) $\dfrac{{72}}{{3125}}$

(C) $\dfrac{{216}}{{625}}$

(D) None of these

(A) $\dfrac{{144}}{{625}}$

(B) $\dfrac{{72}}{{3125}}$

(C) $\dfrac{{216}}{{625}}$

(D) None of these

What happens to the T distribution if the sample size increases?

A random variable has the following probability distribution:

Then the mean of X is

A. 3

B. 1

C. 4

D. 2

$X$ | 1 | 2 | 3 | 4 |

$p\left( X \right)$ | $k$ | $2k$ | $2k$ | $4k$ |

Then the mean of X is

A. 3

B. 1

C. 4

D. 2

The mean weight of $500$ male students in a certain college is $151$ pounds and the standard deviation is $15$ pounds. Assuming the weights are normally distributed, find the approximate number of students weighing

(i) between$120$ and $155$ pounds,

(ii) more than $185$ pounds.

(i) between$120$ and $155$ pounds,

Z | 0.2667 | 2.067 | 2.2667 |

Area | 0.1026 | 0.4803 | 0.4881 |

(ii) more than $185$ pounds.

Two different dice are thrown together, Find the probability that the numbers obtained have

a) Even sum, and

b) Even product

a) Even sum, and

b) Even product

The record of a hospital shows that $10\% $ of the cases of a certain disease are fatal. If $6$ are suffering from the disease, then the probability that only $3$ will die is

$1)1458 \times {10^{ - 5}}$

$2)1458 \times {10^{ - 6}}$

$3)41 \times {10^{ - 6}}$

$4)8748 \times {10^{ - 5}}$

$1)1458 \times {10^{ - 5}}$

$2)1458 \times {10^{ - 6}}$

$3)41 \times {10^{ - 6}}$

$4)8748 \times {10^{ - 5}}$

A purse contains five coins, each of which may be a shilling or a sixpence; two are drawn and found to be shillings: find the probable value of the remaining coins.

What is the probability distribution of rolling a single die?

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